Donald Trump met Viktor Orbán in Florida on Thursday night, just weeks after the Hungarian prime minister met Russia's Vladimir Putin.
His visit to Mar-a-Lago in Palm Beach is the latest in a number of meetings between the two men.
Mr Orbán has publicly endorsed Trump's re-election bid and recently said there was a "very, very high chance" that President Joe Biden would lose the election.
In a tweet, Mr Orbán called the visit "peace mission 5.0", adding:
"We discussed ways to make #peace. The good news of the day: he’s going to solve it!"
The Hungarian leader has been frequently criticised in Europe for his pro-Russian views but remains popular among Trump supporters and US conservatives.
He has also recently met China's Xi Jinping and Volodymyr Zelensky of Ukraine in a self-described "peace" initiative.
On Wednesday, Russian newspaper Izvestia wrote such initiatives were futile, "but Viktor Orbán may pass information he has collected to Trump's team".
Mr Orbán told German media earlier this week that the former US president was a "self-made man" with a "different approach to everything".
A Trump victory in the US election would be "good for the world politics", he added.
"He [Trump] is a man of peace. Under his four-year term he did not initiate a single war, and he did a lot in order to create peace in old conflicts in very complicated areas of the world."
Mr Orbán, whose country currently holds the presidency of the European Union, also criticised the Biden administration for failing to end the conflict in Ukraine.
“I think new leadership will provide new chances," he said.
Mr Orbán was the first and only EU leader to back Trump's bid for presidency in 2016, but had to wait until May 2019 for his first visit to the White House.
Trump has found more time for the Hungarian leader out of power. At the 2022 Conservative Political Action Conference in Dallas, he told cheering delegates: "The globalists can all go to hell... I have come to Texas."
His creation of a similar group in his country, CPAC Hungary, has boosted his relationships further.
In March this year, after meeting Trump in Florida, Mr Orbán posted on X/Twitter: "We need leaders in the world who are respected and can bring peace. He is one of them! Come back and bring us peace, Mr President."
In April this year, Trump sent a short video message to CPAC Hungary, saying he was "honoured to address so many patriots in Hungary... proudly fighting on the front lines of the battle to rescue western civilisation.
"Together we’re engaged in an epic struggle to liberate our nations from all of the sinister forces who want to destroy them.’
He referred to Mr Orbán in the same address as "a great man".
Mr Orbán has boasted that he has created an "illiberal democracy" in Hungary, and claims "progressives" have unleashed a "virus" of "migration, gender, and the woke movement".